One of the general indicators of galactic structure is the mean
surface brightness,
B.
This may be measured by various techniques depending on the chosen
isophotal diameter system. The values of surface brightness presented in
Appendix 2 are determined from

(5.2)

In other words, the integrated apparent magnitude of the galaxy
mHoc is equivalent to the quantity
BT0 in the
RCBG catalogue, corresponding to the area
within the standard isophote at 25m / sq.arc sec.
The transformation from observed diameters and magnitudes to the
(a25, mHoc) system was
described in section 2.2.
As usual, surface brightness is expressed in stellar magnitudes
per square arcsecond.

The differentiation of galaxies by surface brightness,
according to their location in pairs, groups, clusters or the field,
has received insufficient attention in the literature.
Bertola et al. (1971)
noted that among 600
Zwicky (1971)
compact galaxies, the percentage of double and multiple objects was
noticeably higher than among single galaxies.
The possibility of a relation between a galaxy's surface
brightness and the location of its nearest neighbour was considered by
Kormendy (1977),
Zonn (1974) and
Arakelyan and Magtesian
(1981).
These last two studies compared the catalogues of isolated
(Karachentseva, 1973)
and double
(Karachentsev, 1972)
galaxies, but their results appear contradictory. According to
Zonn (1974),
isolated and double spiral galaxies have
the same mean surface brightness, while isolated ellipticals appear
to be somewhat more compact. According to
Arakelyan and Magtesian
(1981),
however, there is no significant difference between elliptical objects
in both catalogues, but an excess surface brightness for the spiral
components of double systems.
A fresh and detailed comparison of the surface brightness for single and
double galaxies was made by
Karachentsev et al. (1985).
In that study, the apparent magnitude and angular diameters of isolated
galaxies were transformed to the common system
(a25, mHoc)
used for double galaxies. The following results are taken from that work.

Figure 38 shows the distribution of single
galaxies (filled circles)
and double galaxies (open circles) of all types, as a function of the
surface brightness calculated according to (5.2).
Both distributions follow a symmetric normal distribution very closely,
with almost identical means (22.72 ± 0.02 for single
galaxies, and 22.69 ± 0.02 for double galaxies), but with
significantly different standard deviations, 0.82 and 0.60 respectively.
Therefore, the presence of close neighbours to a galaxy does not change
the maximum of the distribution but it is possible
that the selection of objects for the catalogue may have excluded
objects with extremely high or extremely low surface brightnesses.

Figure 38.

Excluding contact pairs, for which the respective magnitudes
of the galaxies were calculated from a total magnitude using (2.11),
we constructed the bivariant distribution of
B for
the brighter and fainter components of double systems.
It agreed excellently with the bivariant normal distribution, with
the same mean and standard deviation, and a correlation coefficient of
+0.37.
The high degree of correlation between the surface brightnesses of pair
members may probably be explained as due to their simultaneous formation.
Thus, the correlation of
B
for components of
close pairs is no higher than for wide pairs, since interactions as a cause
of this correlation should not induce any particular value.

The dependence of the mean surface brightness of double and isolated
galaxies on morphological and spectral types is shown in
table 26, which
lists the mean value of each quantity and the standard deviation of the
mean. These data show that the mean surface brightness of double
galaxies decreases monotonically on going from objects with
absorption line spectra to objects with rich emission spectra.
The amplitude of this effect is around 0.45 magnitudes and appears
to be similar for galaxies of different morphological types.
This trend is in agreement with the compendium by
Arakelyan (1975)
in that high surface brightness
is anticorrelated with the presence of strong emission characteristics.
This correlation between spectral types and
compactness may have several causes, which we will now examine.

Table 26.

Figure 39.

Figure 39 shows the distribution of 974 pair
members by absolute magnitude and linear diameter.
The straight line indicates the mean surface brightness,
<B> = 22.69m / sq.arc sec.
Dwarf galaxies are characterized by their greater mean compactness compared
to giant systems. The quantitative relation between mean surface brightness
and linear diameter is

(5.3)

where the diameter A25 is in kiloparsecs.
It follows from table 27 that increasing
richness in the emission line spectrum correlates with a decrease in
both luminosity and linear diameter.
This trend may be explained by postulating that the evolution of dwarf
galaxies proceeds at a slower rate, so that they may normally retain their
original levels of gas and therefore have the raw material for active star
formation at the present epoch.

Table 27.

Consider again the data in table 26, showing the
connection between surface brightness and morphological type.
For components of double systems, the mean surface brightness is
practically the same for all structural types, while
isolated galaxies display a change on going from late
types to early types.
The greatest difference is observed for E and S0 galaxies, and
isolated elliptical galaxies exceed pair
components by a full magnitude in surface brightness. This agrees with
Zonn (1974)
but contradicts
Arakelyan and Magtesian
(1981).
A detailed analysis shows that this last study is strongly
affected by selection.
Among isolated elliptical galaxies a considerable fraction are
listed in the Zwicky catalogue as compact or very compact.
Arakelyan and Magtesian used measurements of galaxy diameters
from the MCG catalogue and therefore did not consider about 60% of
the isolated E galaxies, predominantly the most compact ones, which has
the effect of producing an artificially low estimate of the mean
surface brightness.
It is possible that field elliptical galaxies form a separate
category of objects with structural properties not
encountered among elliptical members of systems. Thus,
Kormendy (1977)
noticed the absence around isolated galaxies
of the extended haloes characteristic of E galaxies with nearby
massive companions.
Kormendy ascribed this property to the recent operation of tidal effects.

Arakelyan and Magtesian
(1981)
demonstrated that the mean surface
brightness of double galaxies decreases with increasing linear
separation, asymptotically approaching the value for isolated
galaxies for X 200 kpc.
We show this dependence for the entire sample of 487 physical double
systems in figure 40 by the filled circles,
with error bars indicating the standard deviation of the mean.
Excluding the single point in the interval 80 - 100 kpc,
these values fall along the descending curve, which drops by
B =
0.7m.
Karachentsev et al. (1985)
examined two effects which might produce such a dependence.

Figure 40.

1. In tight pairs in which the mutual separation of the components is
comparable to their diameters, tidal stripping of the outer
regions of the disk will occur.
The tidal effects increase with greater proximity of the galaxies to
one another, so that members of contact pairs should have the highest
surface brightness.

2. The decreasing number of compact objects on passing from tight pairs
to wide pairs may be a selection effect.
The inclusion of pairs in the catalogue depends on the angular diameters
and apparent magnitudes of the galaxies, as much as on the angular
separation.
Two galaxies with a large separation will have a higher probability
of satisfying the isolation criteria, the larger their angular diameter
is compared to the surrounding field galaxies.
Therefore, galaxies in wide pairs should be distinguished by lower surface
brightness than members of tight pairs.

To estimate such selection we again used the results of the modelling of
the apparent distribution of galaxies and
the resulting selection of double systems (see
section 3.1).
The dependence of mean surface brightness in the model pairs
on their linear separation is shown in figure 40
as diamonds whose height denotes the standard deviation of the mean
(9)
It follows from these results that selection effects in the catalogue
can explain most of the effect observed for the real galaxy pairs.
A small part (~ 0.2m) of the surface brightness for members of
tight pairs with X < 30 kpc might also be explained by tidal
effects during interaction.
However, any dynamical changes in the structure of galaxies are not easy
to distinguish from possible errors in measuring the diameters of galaxies
which are extremely close and, perhaps, overlapping one another.

9 According to the adopted relation
(3.3), the model galaxies have
<B> = 23.63m/sq.arc sec.,
with standard deviation 0.8.
In order to compare the observed and model means we shifted the
model values to a fixed ordinal.
Back.